共查询到20条相似文献,搜索用时 0 毫秒
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David Natroshvili Ioannis G. Stratis 《Mathematical Methods in the Applied Sciences》2006,29(4):445-478
By the potential method, we investigate the Dirichlet and Neumann boundary value problems of the elasticity theory of hemitropic (chiral) materials in the case of Lipschitz domains. We study properties of the single‐ and double‐layer potentials and of certain, generated by them, boundary integral operators. These results are applied to reduce the boundary value problems to the equivalent first and the second kind integral equations and the uniqueness and existence theorems are proved in various function spaces. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
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A. M. Samoilenko 《Ukrainian Mathematical Journal》2011,63(2):278-314
We consider problems of the linear theory of systems of ordinary differential equations related to the investigation of invariant
hyperplanes of these systems, the notion of equivalence for these systems, and the Floquet–Lyapunov theory for periodic systems
of linear equations. In particular, we introduce the notion of equivalence of systems of linear differential equations of
different orders, propose a new formula of the Floquet form for periodic systems, and present the application of this formula
to the introduction of amplitude–phase coordinates in a neighborhood of a periodic trajectory of a dynamical system. 相似文献
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M. Tukhtasinov 《Journal of Applied Mathematics and Mechanics》1995,59(6):935-940
A game with dynamics described by partial differential equations is considered. The equations of the players are additively represented on the right-hand side and are subject to integral or pointwise restrictions. The goal of the first player, who is informed of the instantaneous value of the control of his partner, is to bring the system into an unperturbed state. To solve the problem the decomposition method developed in [1] for a controlled system (with one player) is used. Three combinations of restrictions on the players are considered. In all cases the control of the first player is presented explicitly. The main complication, compared with the problem considered previously [1] is that this control consists of two terms estimated in different norms. 相似文献
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This paper provides a rigorous mathematical treatment of the problem of valuation of a firm in a deterministic, partial equilibrium framework. It is shown that the dividend and arbitrage approaches to valuation are not equivalent in general. A necessary and sufficient condition for their equivalence is also obtained. 相似文献
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A. M. Samoilenko 《Ukrainian Mathematical Journal》1994,46(12):1848-1889
Problems related to perturbation theory of smooth invariant tori of dynamical systems in an-dimensional Euclidean spaceR
n are considered. The clarification of these problems plays an important role for perturbation theory suggested by the author in [1] and extends the scope of its application.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 12, pp. 1665–1699, December, 1994. 相似文献
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Mathematical problems for the next century 总被引:5,自引:0,他引:5
Steve Smale 《Mathematical Intelligencer》1998,20(2):7-15
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M. S. Agranovich 《Functional Analysis and Its Applications》2007,41(4):247-263
For strongly elliptic Systems with Douglis-Nirenberg structure, we investigate the regularity of variational solutions to the Dirichlet and Neumann problems in a bounded Lipschitz domain. The solutions of the problems with homogeneous boundary conditions are originally defined in the simplest L 2-Sobolev spaces H σ . The regularity results are obtained in the potential spaces H p σ and Besov spaces B p σ . In the case of second-order Systems, the author’s results obtained a year ago are strengthened. The Dirichlet problem with nonhomogeneous boundary conditions is considered with the use of Whitney arrays. 相似文献
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O. G. Galkin 《Journal of Nonlinear Science》1994,4(1):127-156
Summary When several oscillators are coupled together and the parameters of their coupling are varied, the oscillators pass through
so-called phase-locked regimes. In physical terms this means that the oscillators tend to synchronize their motion. To describe
this phenomenon, we frame the concepts ofpartial phase andphase-locking. A partial phase of a toral flow puts emphasis on how orbits of the flow drift around the torus in some fixed direction.
The partial phase is locked if it grows in time along some orbit slower than any linear function. When a toral flow is given
by a trigonometric polynomial, its phase-locked regions are quite narrow. With the coupling amplitude increasing, each region
grows in width as some power of the amplitude. That power can be calculated in terms of both the partial phase and degree
of the trigonometric polynomial. 相似文献
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V. M. Entov 《Journal of Mathematical Sciences》1983,21(5):658-664
For the stationary problem of the nonlinear filtration in a bounded domain, from variational principles one establishes a series of statements: for a fixed drop in pressure, an increase in the local filtration resistance or a symmetrization of the domain leads to a decrease of the modified flow rate; at a depression inside the domain of the entrance-surface, the flow and the velocity of the filtration do not decrease at any point of the outgoing surface, etc. When passing to an unbounded domain, it turnsout that at a filtration with a limit gradient, there may exist physically distinct solutions, which are confirmed by examples given In the paper. 相似文献
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Papers on optimal, control theory, reviewed in Referativnyi Zhurnal Matematika during 1971–1975, are surveyed.Translated from Itogi Nauki i Tekhniki, Seriya Matematicheskii Analiz, Vol. 16, pp. 55–97, 1979.We express our deep gratitude to V. V. Al'sevich, I. K. Asmykovich, and T. B. Kopeikinaya, who made available to us a bibliography of papers on several sections, and to T. N. Antonovich, who proved to be of great help to us while working on the survey. 相似文献
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《Communications in Nonlinear Science & Numerical Simulation》2011,16(6):2438-2444
This article sets out mathematical basics of unifying fundamental physical theory, with a single postulate of nonvoid physical vacuum. It will be shown that all basic equations of classical electrodynamics, quantum mechanics and gravitation theory could be derived from two nonlinear equations, which define dynamics of physical vacuum in three-dimensional Euclidean space and, in turn, are derived from equations of Newtonian mechanics. Through the characteristics of physical vacuum, namely its density and propagation velocity of various density’s perturbations, such principal physical conceptions as matter and antimatter, electric, magnetic and gravitational fields, velocity of light, electron, photon and other elementary particles, internal energy, mass, charge, spin, quantum properties, Planck constant and fine structure constant will have clear and sane definitions. 相似文献
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We give the complete solution of a large class of problems in linear system theory, the so-called cover problems. These problems are formulated and solved both in the state-space and in the input-output frameworks. The key concept, which allows the effective parametrization of all solutions of the cover problems, is that of the partial realizations of a sequence of matrices. It is shown that the solutions of the state-space cover problems can be expressed as state spaces of the partial realizations of appropriately defined sequences of matrices, and the solution of the input-output cover problems can be expressed as a simple function of the functions of the partial realizations of the sequences of mentioned above. 相似文献
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Jianyong Qiao 《数学学报(英文版)》1995,11(4):365-371
This paper includes two parts. In the first part, we deal with the relations between the orders, the lower orders and the number of Julia directions of entire functions. In the second part, we deal with the existence of the zeros of a class of meromorphic functions. This class of meromorphic functions has an interesting physical background. 相似文献
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M. Carme Calderer 《Mathematical Methods in the Applied Sciences》1994,17(3):171-188
This article deals with flow phenomena in liquid crystal materials. The model that I analyse is that due to Ericksen for liquid crystals with variable degree of orientation. One of the goals is understanding the role of the order parameter in the model. I examine the multiplicity of solutions, phases, that occur in shear flow regimes and analyse their stability under physically realistic conditions. In particular, I show that ellipticity of the linearized system of governing equations is a consequence of the Clausius–Duhem inequality. 相似文献